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In this paper the effect of donor impurity on the Aharonov–Bohm oscillations of the electronic states in a double quantum ring with Gaussian confinement has been studied. Three different impurity positions: namely in the inner ring, in the outer ring and in the barrier between the rings, have been considered. It is shown that the energies of the two lowest states are almost constant, while for the higher levels the Aharonov–Bohm oscillations are observed. The obtained results indicate on the possibility of the effective control of the quantum states by means of donor impurity and external magnetic field.